Average Error: 0.1 → 0.1
Time: 18.7s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(y - \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot y + \log \left(\sqrt[3]{y}\right) \cdot y\right) + \log \left(\sqrt[3]{y}\right) \cdot y\right) + 0.5 \cdot \log y\right)\right) - z\right) + x\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(y - \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot y + \log \left(\sqrt[3]{y}\right) \cdot y\right) + \log \left(\sqrt[3]{y}\right) \cdot y\right) + 0.5 \cdot \log y\right)\right) - z\right) + x
double f(double x, double y, double z) {
        double r14235448 = x;
        double r14235449 = y;
        double r14235450 = 0.5;
        double r14235451 = r14235449 + r14235450;
        double r14235452 = log(r14235449);
        double r14235453 = r14235451 * r14235452;
        double r14235454 = r14235448 - r14235453;
        double r14235455 = r14235454 + r14235449;
        double r14235456 = z;
        double r14235457 = r14235455 - r14235456;
        return r14235457;
}
↓
double f(double x, double y, double z) {
        double r14235458 = y;
        double r14235459 = cbrt(r14235458);
        double r14235460 = log(r14235459);
        double r14235461 = r14235460 * r14235458;
        double r14235462 = r14235461 + r14235461;
        double r14235463 = r14235462 + r14235461;
        double r14235464 = 0.5;
        double r14235465 = log(r14235458);
        double r14235466 = r14235464 * r14235465;
        double r14235467 = r14235463 + r14235466;
        double r14235468 = r14235458 - r14235467;
        double r14235469 = z;
        double r14235470 = r14235468 - r14235469;
        double r14235471 = x;
        double r14235472 = r14235470 + r14235471;
        return r14235472;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x + \left(y - \mathsf{fma}\left(0.5 + y, \log y, z\right)\right)}\]

  3. Taylor expanded around inf 0.1

    \[\leadsto x + \color{blue}{\left(\left(y \cdot \log \left(\frac{1}{y}\right) + \left(y + 0.5 \cdot \log \left(\frac{1}{y}\right)\right)\right) - z\right)}\]

  4. Simplified0.1

    \[\leadsto x + \color{blue}{\left(\left(y - \log y \cdot \left(y + 0.5\right)\right) - z\right)}\]
  5. Using strategy rm

  6. Applied distribute-rgt-in0.1

    \[\leadsto x + \left(\left(y - \color{blue}{\left(y \cdot \log y + 0.5 \cdot \log y\right)}\right) - z\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.1

    \[\leadsto x + \left(\left(y - \left(y \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + 0.5 \cdot \log y\right)\right) - z\right)\]

  9. Applied log-prod0.1

    \[\leadsto x + \left(\left(y - \left(y \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + 0.5 \cdot \log y\right)\right) - z\right)\]

  10. Applied distribute-lft-in0.1

    \[\leadsto x + \left(\left(y - \left(\color{blue}{\left(y \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)} + 0.5 \cdot \log y\right)\right) - z\right)\]

  11. Simplified0.1

    \[\leadsto x + \left(\left(y - \left(\left(\color{blue}{\left(y \cdot \log \left(\sqrt[3]{y}\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)} + y \cdot \log \left(\sqrt[3]{y}\right)\right) + 0.5 \cdot \log y\right)\right) - z\right)\]

  12. Final simplification0.1

    \[\leadsto \left(\left(y - \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot y + \log \left(\sqrt[3]{y}\right) \cdot y\right) + \log \left(\sqrt[3]{y}\right) \cdot y\right) + 0.5 \cdot \log y\right)\right) - z\right) + x\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))